Algebra Examples

$y = 7$

Step 1

Since $x = r \cos (θ)$ , replace $x$ with $r \cos (θ)$ .

$y = 7$

Step 2

Since $y = r \sin (θ)$ , replace $y$ with $r \sin (θ)$ .

$r \sin (θ) = 7$

Step 3

Divide each term in $r \sin (θ) = 7$ by $\sin (θ)$ and simplify.

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Step 3.1

Divide each term in $r \sin (θ) = 7$ by $\sin (θ)$ .

$\frac{r \sin (θ)}{\sin (θ)} = \frac{7}{\sin (θ)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\sin (θ)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{r \sin (θ)}{\sin (θ)} = \frac{7}{\sin (θ)}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{7}{\sin (θ)}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Separate fractions.

$r = \frac{7}{1} \cdot \frac{1}{\sin (θ)}$

Step 3.3.2

Convert from $\frac{1}{\sin (θ)}$ to $\csc (θ)$ .

$r = \frac{7}{1} \csc (θ)$

Step 3.3.3

Divide $7$ by $1$ .

$r = 7 \csc (θ)$